In the next step, the global dataset is generated based on the \(ER\)  DAGs, and by employing the internal sample generation mechanism of [1]}. We utilize the data generation method to sample categorical data with 10 categories in different sizes for both interventional and observational data. The generated global dataset \(D\)  is evenly distributed among clients in multi-client setups. However, the distribution of the global dataset could either be horizontal or vertical, meaning that a client may receive interventional samples for all intervened variables or only a subset of those variables.
